Maximum Inter-story Drift Ratio Research Articles

Seismic performance analysis of multi-story steel frames equipped with FeSMA BRBs

Buckling-restrained braces (BRBs) have been widely used in seismic prone areas around the world. However, one major problem associated with the steel BRB frames is the excessive residual deformation under strong earthquakes, mainly due to the low post-yield stiffness ratio of the steel BRBs. Recently, the community has fabricated the iron-based shape memory alloy (FeSMA) BRBs, which exhibited full hysteresis with high post-yield stiffness ratios, but the seismic behavior of the FeSMA BRB frames still remains unknown. As such, this paper conducts seismic performance analysis of multi-story steel frames equipped with the FeSMA BRBs, through a comparison with those equipped with conventional steel BRBs. Incremental dynamic analysis (IDA) is further conducted to establish the probability seismic demand models. Based on the IDA data, bivariate fragility analysis is conducted to quantify the probability of exceedance, conditioned on various limitations of the maximum and residual interstory drift ratios. According to current analysis, it indicates that both the maximum interstory drift ratios and the maximum floor accelerations are comparable between these two types of BRB frames. The major advantage of the FeSMA BRBs over the steel BRBs is that the former can better control residual interstory drift ratios.

Blast Performance of Steel Frames Equipped with NiTi SMA Bolts: Design Procedure and Numerical Evaluation

This study evaluated the performance of smart steel moment-resisting frame structures (MRFs) equipped with nickle titanium shape-memory alloy (NiTi SMA) connection systems subjected to blast overpressure. A total of five NiTi SMA–based connections were designed conforming to current European standards, and their numerical models were developed. To study the effect of number of parameters, e.g., section profiles, bolt diameter, and bolt preload, a parametric study has been conducted on NiTi SMA–based connections. The numerical models were validated against experimental data, and key design procedures have been proposed. A simplified Kingery blast calculation framework was adapted to determine the blast reflected overpressure profile. The strength of the NiTi SMA bolts and steel components were adjusted due to a high strain rate of blast loading. Four MRFs equipped with a NiTi SMA–based connection were designed with different heights. Global-level transient analyses were performed on the MRFs subjected to blast overpressure. The results showed that in addition to relatively large maximum interstory drift ratio, the NiTi SMA–based connections significantly reduced the residual interstory drift ratio compared with the steel bolted connection system counterpart. The results also revealed that the proposed key design procedures are essential to emphasize the role of NiTi SMA bolts.

Risk assessment of CLT-RC hybrid building: Consideration of earthquake types and aftershocks for Vancouver, British Columbia

Tall-timber buildings using cross-laminated timber (CLT) have become a viable sustainable system. This paper presents seismic vulnerability and risk assessment of a 10-story CLT-reinforced concrete hybrid building. The building is designed for the seismicity of Vancouver, and detailed 3D finite element model is developed in OpenSees. The evaluation is undertaken within a performance-based earthquake engineering framework in which seismic demand limits are defined with respect to the earthquake return periods. Two engineering demand parameters, i.e. maximum inter-story drift ratio in both X and Z directions, as well as their combination are considered. Using 30 mainshock and mainshock-aftershock earthquake records (two horizontal components per record), multiple stripe analysis and cloud analysis are performed, and the corresponding fragility and risk are quantified. In addition efficiency of different intensity measures are considered. The vulnerability and risk assessment results show viability of the hybrid building in high seismic zones.

Seismic design and performance of a steel frame-shear plate shear wall with self-centering energy dissipation braces structure

The steel plate shear wall with self-centering energy dissipation braces (SPSW-SCEDB) is a new seismic lateral resistant component. This paper outlines the performance requirements of the steel frame-shear plate shear wall with self-centering energy dissipation braces (SF-SCSPSW) structure and presents a direct displacement-based seismic design method for the structure. A combined strip model of the SPSW-SCEDB that considers the effect of the bolted connection on the wall plate is established. The comparison of the simulated and experimental results shows that the model can accurately predict the strength and hysteretic behavior under cyclic loading. The 8- and 15-story prototype buildings were designed using the presented method. The results of nonlinear dynamic analysis showed that larger inter-story deformations occurred on the lower floors, and the inter-story ratios gradually decreased with an increase in the number of floors. The maximum inter-story drift ratio (1.73%) of the 8-story structure under mega earthquakes and the maximum residual drift ratio (0.018%) of the 15-story structure under large earthquakes were less than the limit values (2% and 0.5%). Local yielding occurred between the brace connection and the column under mega earthquakes, but the columns remained in an elastic state. The seismic responses of the SPSW-SCEDBs in the two structures met the performance requirements of being elastic and suffering light and moderate and serious damage under frequent, medium, large, and mega earthquakes, respectively. The effectiveness of the proposed design method was verified.

An energy-based analysis framework for soil structure interaction systems

Presented is an energy-based analysis and design framework for soil structure interaction system. Theoretical formulation based on thermodynamics and engineering mechanics for calculating energy dissipation in soil and structural elastic plastic finite elements is presented and discussed. The importance of incorporation of plastic free energy, that ensures nonnegative incremental energy dissipation, also known as the second law of thermodynamics, is emphasized. For application to practical engineering problems, the presented framework is implemented in the Real-ESSI Simulator and visualized using ParaView. In order to illustrate the proposed framework, a practical model composed of a reinforced concrete frame structure, underlying soil, and soil-foundation interface is developed and analyzed. Elastic-plastic material model and viscous, Rayleigh damping parameters are calibrated to represent typical realistic cases. Spatial and time distribution of energy dissipation density is analyzed and discussed. Locations with high plastic energy dissipation, used as a proxy for material and structural damage are identified. In addition, locations of high plastic energy dissipation within soil and soil-foundation interface, that are used to dissipate seismic energy before it reaches structure, are also identified. Influences of input seismic motion scale and design variation on system performance are investigated. It is shown that traditional displacement-based design parameters, such as peak displacement and maximum interstory drift ratio, could underestimate the change of system performance when different seismic motion scale or structural design are used.

Dual-Objective Control of Maximum and Residual Drift Ratios of Super-Tall Buildings Based on Self-Centering Energy Dissipation Outriggers

It is critical to ensure the seismic resilience of super-tall buildings using high performance materials. The seismic resilience of these buildings can be enhanced by simultaneously controlling the maximum and residual inter-story drift ratios. To realize such dual-objective control, a prevailing trend is to adopt self-centering energy dissipation outriggers. In this study, taking a real engineering practice as the prototype building, super-tall building study cases with energy dissipation outriggers, and with self-centering energy dissipation outriggers are designed. Based on nonlinear time-history analysis, the seismic performances of these study cases are evaluated and compared with emphasis on the maximum, and residual inter-story drift ratios. The dual-objective control effect of self-centering energy dissipation outriggers and energy dissipation outriggers are analyzed and compared. The results indicate that self-centering energy dissipation outriggers are more effective than energy dissipation outriggers for achieving the dual-objective control of the maximum and residual drift ratios of super-tall buildings.

Higher mode effects for mid-rise buildings in relation to far fault ground motion characteristics

In this research study, activation of higher modes as functions of several ground motion parameters is studied. For this purpose, MDOF reinforced concrete shear frame with 20 storey are modeled to represent medium height buildings. Then, fast nonlinear time history analyses of the MDOF shear frame are conducted to observe the effects of the selected parameters on the activation rates of higher modes. The parameters used as ground motion characteristics are the PGA/PGV and PGD/PGV ratios of ground motion records. These parameters are known to control the length of the acceleration and displacement sensitive regions of a response spectrum, respectively. Effect of these parameters on the activation of higher structural modes are considered for ordinary far fault ground motion records without pulse like characteristics. The differences obtained in terms of the maximum inter-story drift ratio and shear force distribution along the height of the building are presented quantitatively to give detail about the effectiveness of the higher modes as a function of ground motion characteristic. The analyses results revealed that the effect of higher modes vary significantly in relation to considered ground motion characteristics.

Earthquake‐resistant subsystem stiffness demand estimate of frame–core tube structures with mass and stiffness nonuniformities

SummaryTo develop reasonable structural schemes of frame–core tube structures in the preliminary seismic design, a stiffness estimation of the main subsystems, that is, core tube, frame, and outrigger, is provided through the rocking model (RM) and flexural–shear coupled model (FSM). A nonuniform RM (RM‐MS) is proposed with the dual nonuniform distributions of mass and subsystem stiffness corresponding to those of the nonuniform FSM (FSM‐MS). The dynamic properties of the RM‐MS are semianalytically solved with the general solution for the free vibration of the nonuniform flexural beam and the rotational stiffness matrix of outriggers. The relation between the FSM‐MS and RM‐MS is established based on the first two vibration periods and nonlinear fitting and extended to present a subsystem stiffness estimation strategy with target maximum interstory drift ratios (IDRmax) and overturning moment distribution ratios (RM,B). The feasibility and effectiveness of the strategy are fully demonstrated by three cases with different target RM,B. RM‐MS effectively controls structural lateral stiffness of FSM‐MS in advance. With the target RM,B beyond the feasible range, it is necessary to adjust the first two vibration periods estimated by FSM‐MS. Compared with the axial rigidity of frame columns, the flexural rigidity of outriggers shows higher priority to increase RM,B.

Seismic performance evaluation of glulam structures with either braced frames or knee-braced frames as the main lateral load resisting system

The glulam knee-braced frames and braced frames are both conventional structural systems that are generally adopted in engineering practice. However, it remains a question what are the advantages and challenges of the knee-braced frames compared with the braced frames and how to choose the appropriate lateral-resisting structures for the projects under a given design requirements. This paper provides numerical models of 3- story, 5- story, 6- story and 9- story glulam braced frames and glulam knee-braced frames with the same architectural plan view. Increment dynamic analysis (IDA) is performed to determine the limit state of MaxISDR (maximum inter-story drift ratio) for the glulam braced frames and the glulam knee-braced frames under different seismic hazard levels, i.e., IO (Immediate Occupancy), LS (Life Safety), CP (Collapse Prevention) and CD (Complete Destroy). Fifty earthquake records are adopted for the subsequent probabilistic seismic demand analysis based on the MaxISDR and ResISDR (residual inter-story drift ratio) damage indices. The fragility curves of these two types of structures are highlighted. The results show that, the limit state of MaxISDR for the glulam braced frames under the IO, LS, CP and CD hazard level are recommended to be 0.6%, 1.2%, 2.0% and 3.5% respectively. The limit state of MaxISDR for the glulam knee-braced frames under the IO, LS, CP and CD hazard levels are recommended to be 1.0%, 2.0%, 3.2% and 5.5% respectively. In addition, for the structural height that below 6 stories, the knee-braced frames have lower probability of MaxISDR exceedance than the braced frames under the earthquake with high PGA and lower probability of ResISDR exceedance than the braced frames. However, for the structural height of 9-stories, the recoverability of the knee-braced frames decreases rapidly. Adding some braces to the knee-braced frames can be a good solution to increase the lateral stiffness of the structures. The comparison results may provide technical reference for the structural design of glulam structures.

Seismic retrofit of a soft first-story building using viscoelastic dampers considering inherent uncertainties

The mechanical properties of viscoelastic dampers (VED) generally vary depending on the loading conditions such as input frequency, amplitude, and temperature, which makes the conventional modeling approach of using constant material properties highly inaccurate. This study develops the kriging model, which is a powerful tool when there is a limited number of experimental data available, for VED made of high energy dissipation acrylate and nitrile butadiene rubber-based viscoelastic materials. The coefficients of determination (R2) of the storage and loss moduli predicted by the kriging model turns out to be 0.9805 and 0.9868, respectively, which proves that the model predictions for the test data are quite accurate. Fuzzy random analysis of a soft first-story building is carried out to investigate the effectiveness of the damper in uncertain conditions. The results show that when the informal uncertainty is minimum, the maximum inter-story drift ratio of the example structure is reduced from 1.6% to 1.0% after installation of the dampers; when the informal uncertainty is maximum, the maximum inter-story drift ratio of the building is reduced from 5.0% to 2.6% after the retrofit.

Nonlinear seismic performance study of D‐type self‐centering eccentric braced frames with sliding rocking link beams

AbstractThis paper presents a nonlinear numerical simulation study of the D‐type self‐centering eccentric braced frame system with a sliding rocking link beam (SCEBF‐SRL) to overcome the beam‐growth problem. The re‐centering capability of such SCEBF‐SRLs is enabled by post‐tensioned (PT) steel‐stranded cables. Replaceable hysteretic dampers termed RHD are used as seismic fuse devices for energy dissipation, while the friction force due to the relative movement of the sliding rocking link beam inside the column corbels would also contribute to the energy dissipation capacity of the system. Analytical load versus displacement relationships of an SCEBF‐SRL module frame were formulated and cross‐validated with nonlinear finite element (FE) analysis results. The seismic performance of the proposed system was studied through nonlinear static and dynamic analysis of three‐ and six‐story prototype SCEBF‐SRL buildings. A set of twenty‐two far‐field ground motions from the FEMA P695 database was adopted for nonlinear dynamic analysis (NDA). NDA results revealed that the ensemble median of the maximum inter‐story drift ratios (IDRs) of both SCEBF‐SRL prototypes were less than 1.4% and 2.0% at the design basis earthquake (DBE) and the risk‐targeted maximum considered earthquake (MCER) levels, respectively. Additionally, both SCEBF‐SRL buildings fully re‐centered themselves at MCER with negligibly small residual drift (<0.01%). The parametric study results suggest that with an energy dissipation ratio, between 25% and 60% and a minimum stiffness ratio of 5%, the ensemble median of the maximum IDR of the considered prototype building could be made less than 1.5% and 2.3% at DBE and MCER levels, respectively.

Study of Building Safety Monitoring by Using Cost-Effective MEMS Accelerometers for Rapid After-Earthquake Assessment with Missing Data.

Suffering from structural deterioration and natural disasters, the resilience of civil structures in the face of extreme loadings inevitably drops, which may lead to catastrophic structural failure and presents great threats to public safety. Earthquake-induced extreme loading is one of the major reasons behind the structural failure of buildings. However, many buildings in earthquake-prone areas of China lack safety monitoring, and prevalent structural health monitoring systems are generally very expensive and complicated for extensive applications. To facilitate cost-effective building-safety monitoring, this study investigates a method using cost-effective MEMS accelerometers for buildings’ rapid after-earthquake assessment. First, a parameter analysis of a cost-effective MEMS sensor is conducted to confirm its suitability for building-safety monitoring. Second, different from the existing investigations that tend to use a simplified building model or small-scaled frame structure excited by strong motions in laboratories, this study selects an in-service public building located in a typical earthquake-prone area after an analysis of earthquake risk in China. The building is instrumented with the selected cost-effective MEMS accelerometers, characterized by a low noise level and the capability to capture low-frequency small-amplitude dynamic responses. Furthermore, a rapid after-earthquake assessment scheme is proposed, which systematically includes fast missing data reconstruction, displacement response estimation based on an acceleration response integral, and safety assessment based on the maximum displacement and maximum inter-story drift ratio. Finally, the proposed method is successfully applied to a building-safety assessment by using earthquake-induced building responses suffering from missing data. This study is conducive to the extensive engineering application of MEMS-based cost-effective building monitoring and rapid after-earthquake assessment.

Appropriate intensity measures for probabilistic seismic demand estimation of steel diagrid systems

Performance-based earthquake engineering (PBEE) predicts the performance of structures subjected to earthquake ground motions to improve seismic risk mitigation decisions. In PBEE, intensity measures (IMs) are employed as a link between earthquake hazard and seismic response. To the best of the authors' knowledge, investigation of the appropriate IMs for the probabilistic seismic demand evaluation of steel diagrid systems has not been presented in literature so far. In this study, the efficiency, practicality, proficiency, sufficiency, and scaling robustness of 38 candidate IMs for estimating the seismic response of low- to high-rise steel diagrid systems are investigated. Finite-element models of the structures are performed in OpenSees software and subjected to incremental dynamic analysis (IDA) using 22 far-field earthquake records. The whole response of the investigated diagrid systems is captured in terms of maximum inter-story drift ratio (MIDR). The appropriate IMs among the candidate IMs for steel diagrid systems are identified utilizing the concepts of efficiency, practicality, proficiency, sufficiency, and scaling robustness. The regression analysis results showed that peak ground velocity (PGV) and the ratio of PGV to peak ground acceleration (i.e., PGV/PGA) are the most appropriate IMs for seismic response prediction of steel diagrid systems under far-field ground motions. Furthermore, the collapse fragility curves, as well as drift hazard curves, were obtained based on various IMs. It was observed that the proposed IMs reduce the uncertainty in fragility curves. Also, it was concluded that seismic IM has a significant impact on the structural response hazard of steel diagrid systems.

Application of Mean-covariance Regression Methods for Estimation of EDP|IM Distributions for Small Record Sets

ABSTRACT The performance of several regression methods is investigated to estimate the distribution of engineering demand parameters conditioned on intensity measures (EDP|IM) for small record sets. In particular, the performance of the multivariate ordinary least squares (OLS), a simultaneous mean-variance regression (MVR) done by a penalized weighted least-square loss function, and a mean-covariance/variance regression based on expectation maximization method (EM) are assessed. The efficiency of the introduced methods is compared with FEMA-P58 methodology. Performance assessment of EM and MVR methods shows that the overall increase in efficiency is about 25–45% for maximum inter-story drift ratios, and 30–50% for maximum absolute floor acceleration.

Seismic fragility of structures with energy dissipation devices for mainshock-aftershock events

This paper presents a mainshock-aftershock seismic fragility and collapse capacity assessment of reinforced concrete (RC) structures retrofitted with a hybrid damper composed of a steel slit plate and friction pads. Three and eight-story RC buildings are designed and assessed before and after retrofit considering the aftershocks effect. Non-linear time-history response analysis (NLTHA) using twelve natural earthquake sequences are used to produce incremental dynamic analysis (IDA) curves to obtain the median collapse capacity of the structures. Three different damage state (DS) levels are used for the mainshock ground excitation to quantify the scale factors required for conducting the aftershock IDAs. The maximum inter-story drift ratio (MIDR) is used as the main engineering demand parameter. The study shows the importance of considering the aftershock in the seismic assessment process of RC structures. The un-retrofitted structures are found to experience a high level of deterioration under aftershock event which is not considered in the design stage. The findings of the study reveal that the mainshock-aftershock sequence responses of the retrofitted structures show better performance in terms of the median collapse capacity and the seismic fragility compared to the un-retrofitted ones.

Seismic fragility analysis of RC frame-shear wall structure under multidimensional performance limit state based on ensemble neural network

An improved seismic fragility analysis method without any assumption on the distribution of the target engineering demand parameter is proposed based on an ensemble neural network. Firstly, a multidimensional performance limit state function is introduced to evaluate both the structural and non-structural performance. Next, an ensemble neural network, which is defined as a weighted average of three artificial neural networks, is trained to predict the index of the structure subjected to any seismic ground motion. A new index derived from the multidimensional performance limit state function is defined as the neural network output. Finally, the fragility curves are obtained by means of Monte Carlo simulation with high computational efficiency with the help of the ensemble neural network. It is applied to a reinforced concrete frame-shear wall structure, and the maximum inter-story drift ratio and the peak floor acceleration are selected as two engineering demand parameters. The results indicate that, the prediction accuracy of the ensemble neural network is higher than other three neural networks. If only a single neural network is used, the obtained fragility curves may have much error. Compared to the traditional multidimensional probabilistic seismic demand model based on the lognormal distribution assumption, the proposed method can give more credible seismic fragility curves.

Fragility Comprehensive Assessment of Low-Rise Cold-Formed Steel Framed Wall Structure Subjected to Wind Load

This paper presents a comprehensive assessment method of the fragility of low-rise cold-formed steel (CFS) framed wall structures subjected to wind hazards considering the fragility of both the main structure and the cladding system. The effects of wind directions on the fragility of CFS framed wall structures were also studied. For the main structure, the fragility curve is established using the maximum interstory drift ratio (ISDRmax) as the performance index for assessing the wind fragility of the structure. For the cladding system, the probabilistic models of the wind load and the cladding component resistance are established based on Monte Carlo simulation, and then methods for the fragility assessment of single cladding components and the cladding system under wind hazards considering the influence of the number and arrangement of the cladding components are proposed. The results indicated that, under strong wind, the cladding system may be damaged before the required wind resistance capacity of the main structure is exhausted. In particular, the roof sheathing is the most prone to damage, followed by the stud wall. That is, before the main structure is severely damaged or collapses, the cladding systems may be severely damaged, rendering the structure unusable. Therefore, the comprehensive assessment of the fragility of this type of structure subjected to wind hazard considering the fragility of both the main structure and the cladding system is more accurate. This study is of great significance for the improvement of the wind resistance performance of CFS structures and the popularization of this type of structure.

Component deformation-based collapse evaluation of RC frameunder different collapse criteria

Developments in performance-based earthquake engineering have emphasized the importance of evaluation of structural collapse resistance. Several collapse criteria were proposed to define structural collapse in various perspective. In this paper, collapse resistant capacity of ductile reinforced concrete (RC) frame was evaluated using different collapse criteria. Since most of the criteria focus on overall structural response, a component deformation-based method was adopted to describe the damage in component level. Incremental dynamic analysis (IDA) of a 6-story ductile RC frame conforms to current codes was conducted in OpenSEES. The collapse resistant capacity under different collapse criteria was compared. Moreover, relationship between overall structural response and the distribution of damaged components were discussed through the component deformation-based method. It was indicated that the story of maximum inter-story drift ratio is neither consistent with the one which is most seriously damaged nor with the story of maximum residual inter-story drift ratio. Furthermore, the component deformation-based method can depict structural damaged state and formation of collapse mechanism more reasonably. The analysis result evidences that structure conforms to current code have the good ductility and hardly reaches physical collapse under rare earthquake, however, the structure is more likely to be demolished due to unacceptable residual deformation.

Comparison of the seismic‐resilient design of seismically isolated reinforced concrete frame structures using two codes

SummaryResilience‐based seismic design of buildings using seismic isolation has become a critical issue. Currently, there are two design codes for isolated structures in China, exhibiting significant differences. It is critical to investigate the resilience‐based design of isolated buildings using these codes. Hence, using reinforced concrete (RC) frame buildings as an example, two groups of buildings with different heights were designed to achieve the lower limit of seismic performance given in two codes. Although different requirements for acceptable isolation efficiency control this design, the seismic resilience levels were assessed to be Level 2 for all cases. The controlling index is the total repair time, which is dominated by the maximum inter‐story drift ratio (MIDR). Meanwhile, significant differences in design results and resilience performance between two codes were identified. Subsequently, the highest resilience performance (i.e., Level 3) oriented optimization was conducted, and the correspondingly designed schemes using two codes were compared; it was identified that the MIDR of the superstructure requires controlling to approximately 0.23% for such a design using both codes, and the differences between two codes became negligible. The research outcome will assist in providing a useful reference for the seismic‐resilient design of base‐isolated RC frame structures.

Analytical study of stiffened multibay planar coupled shear walls

Placing stiffening coupling beams at some levels of a coupled shear wall (CSW) structure is a proper way to enhance the coupling effects and reduce the interstory drifts of the structure. The resulting structural systems are called stiffened CSWs. To date, rigorous closed-form solutions for stiffened multibay planar CSWs subjected to lateral loading have not yet been derived. To solve this problem, a new approach based on the displacement method was proposed to establish the governing equations and boundary conditions, in which the rotation of the cross sections of walls was decomposed into two components: one associated with the axial deformations of wall piers and the other associated with the flexural and shear deformations of coupling beams. The closed-form solutions for the lateral displacement and rotation components were derived for standard load cases, which were verified to have high accuracy. The analytical solutions indicate that the distributions of the lateral displacements and rotation components along the structural height only depend on four dimensionless parameters, which are related to the composition ratio of the moment of inertia of the wall piers about their common centroid, the ratios of the span stiffness of the ordinary coupling beams to that of the wall piers and that of the stiffening beams, and the relative stiffness level, respectively. Parametric studies were further conducted to investigate the influence of these governing parameters on the degree of coupling, interstory drift ratios, and rotation components. It was found that the optimal stiffening levels for achieving the maximum degree of coupling commonly range from 0.06 to 0.50, and those for achieving the minimum of the maximum interstory drift ratio commonly range from 0.59 to 0.80. These findings provide useful implications for the optimization design of stiffened multibay CSWs.